You swipe up and remove the application from the stack, all processes of the application is killed.
Background processing has strict limits, and you need permissions to run longer than that, and for some use cases, there are no recourse. OS swaps you out or freezes the app.
If you want an app to work in the background, don't kill it, period. Push notifications are handled by the OS and is not hindered by this.
Think for example reddit, you open a thread, how do you go back?
You open the "reply window, now ho you ho back? Maybe close it directly?
I Android this is all handled by the same function and is often ranked as the most frustrating design choice in IOS
They all are very different applications and have very different designs, yet the arrow is there.
To be honest, I baffled at your question for a second or so, because I never thought about that, yet the method is so universal that I was not thinking about it at all.